[Smt-talk] Abbreviated Labels of Seventh Chords

Nicolas Meeùs nicolas.meeus at paris-sorbonne.fr
Sun Feb 12 10:44:44 PST 2012

It occurred to me also that some of Catel's notation can be found in CPE 
Bach -- with important differences, though. CPE's 4+ is a 4 with an 
extended horizontal line and a stripe crossing it. Catel writes +4, or 
even such combinations as +/2 (meaning +4/2) or +/4/3 (obviously for 
+6/4/3). Both CPE and Catel use 2 alone to refer to the third inversion 
of a seventh which is not a dominant. For the diminished 5th, CPE writes 
5b; barred figures for him usually indicate raised intervals and his 4+ 
may be a mere barred (i.e. raised) 4. (On the other hand my cursory 
glance through the /Versuch/ did not allow me to find a barred 5). For 
Catel, on the other hand, a barred figure is a diminished interval.
     I believe that Catel's intention was to specifically indicate one 
or the other note of the augmented 4th/diminished 5th characteristic of 
the dominant, by either a + or a barred 5. This was never stated, that I 
know, neither by him nor by his followers; but the Paris Conservatoire 
makes such a point to distinguish the "natural" (dominant) seventh from 
any other ("septièmes d'espèce") that the intention, conscious or not, 
seems unescapable.

Writing harmony in open score and C clefs (more precisely, chiavi 
naturali) was standard practice in the Conservatoire. We still did that 
in the Brussels Conservatoire during my studies (hum! some time ago...), 
working the basses and sopranos given at late-19th-century final exams 
in the Paris Conservatoire. For us, at least, voice-leading 
considerations were indeed paramount, but boiled down to avoiding 
parallel or "hidden" fifths and octaves. There was no question of 
melodic fluency (on the contrary: the exercises often requested tricky 
voice movements). We did try imitations (which the exercises often made 
possible). I always had the feeling that our classes were not in 
harmony, but in some kind of free tonal counterpoint, a counterpoint 
that reduced to avoiding parallels (one never spoke of good or bad 
successions of chords, my teacher and most of my colleagues students new 
nothing of harmonic functions, nor even of Roman numerals).

Nadia Boulanger's teaching of harmony does not seem very different from 
that. I presume that she was able to turn to musical advantage what in 
our case sounded musical nonsense. What we did had no style at all, and 
was not meant to; but it did more than earning us the right to be free, 
it also shew us how to be free and really gave us a facility of writing. 
A lot is done today in the Conservatoire to learn writing "in the style 
of", to write pastiches "à la Fauré", "à la Debussy", "à la Messiaen", 
etc. This may give the students the (false) impression of writing "real" 
music, but certainly does not help understanding what the Masters did 
(one does not write "à la Beethoven", that I know: it would be too 

Nicolas Meeùs
Université Paris-Sorbonne

Le 11/02/2012 16:32, Donna Doyle a écrit :
> As a former Boulanger student, overloaded these days with teaching, I 
> nevertheless make stabs at completing my dissertation
> on Boulanger's methods and their tradition. All the materials I have 
> that are associated with her (incl basses and figures I copied from 
> her sheets and my realizations approved by her), show the 
> Conservatoire's figured bass tradition, e. g., 4+, without the 2,//
> for V4/2. I believe this notation comes not only from Catel, as you 
> point out, Nicholas, but from CPE.  As Phil Duker offered,
> CPE lists several figures for this disposition (p 252). Indeed, on p 
> 260 CPE reminds readers that 4+ is an abbreviated 6/4/2.
> NB also used 7 over + for V7, 6 over barred 5 for 6/5 and only +6 for 
> 4/3. The leading-tone chord was considered a
> "dominant FO" (fundamental omitted). She used few 
> romans. Voice-leading was paramount. She insisted on
> realizations written in open score, C clefs, and played for her. (And 
> the performance had better be musical or she
> would jump in her chair. ["But, my dear!  Zhe poor tenor!"]) She 
> delighted in various realizations, especially those
> employing imitation and little canons between the voices--techniques 
> of her oral tradition. And, of course,
> this was done in conjunction with intense ear training, enabling us to 
> see what we hear and hear what we see.
> For Boulanger, as with CPE, bass realization was an aspect of 
> Accompaniment. It seems to me that our insistence on elegantly
> logical numbering systems is defying the rich, sometimes messy nature 
> of this once vibrant practice. Apart from Schenkerian analysis, 
> figured bass is a chord-labeling shadow of its former self. 
>  Let's restore its life! (Perhaps not for undergraduates,
> but in graduate curricula, for composers, theorists, organists, maybe 
> also pianists and conductors.) As NB said, "It's not
> that you're going to write in this style. But after working with it, 
> you'll have earned the right to be free." Isn't this what 
> composers/theorists/performers used to do? I find it remarkable that 
> NB, despite being called "French provincial,"
> continued to transmit this tradition into the 1970s.
> Best,
> Donna Doyle
> Queens College CUNY
> On Feb 9, 2012, at 3:40 AM, Nicolas Meeùs wrote:
>> The French tradition, that of the Paris Conservatoire, is to write +4 
>> in this case, the + meaning that the 4 is the leading tone 
>> (similarly, one would write +6 in second inversion). This tradition, 
>> which is not mine and against which I am trying to fight in Paris, 
>> has several drawbacks, one of them being that the French use labels 
>> that hardly anyone else understands.
>>     I wondered about the origin of this figuring, without performing 
>> a thorough research. It certainly goes back to Catel's treatise, and 
>> perhaps earlier. The + sign is in origin merely a stylized #. Catel 
>> makes use of it (and of the barred 5) with the specific (although 
>> unstated) intention of specially labeling dominant seventh chords, 
>> the ones that he considers "natural", all positions of which always 
>> have either a + or a barred 5 (from fundamental position to third 
>> inversion: +3; 6/5barred; +6, +4; this is tricky, because 4/3 becomes 
>> +6, 2 or 4/2 becomes +4). Applied dominants are labeled in the same 
>> way, with the other perverse effect that French students see 
>> modulations everywhere (as the French did since François Campion in 
>> 1716: /tout diese extraordinaire fait sortir du ton/, "any accidental 
>> sharp leads outside the tonality").
>>     Labeling third-inversion dominants as V4/2 may result from an 
>> attempt to reconcile the two systems. In this respect, I'd be pleased 
>> to know how Nadia Boulanger labeled chords, if anyone on this list 
>> knows (it has been discussed here some time ago that her teaching of 
>> harmony followed the tradition of the Conservatoire, but her 
>> ciphering was not specifically discussed, that I remember).
>> My own view about the labeling of seventh chords is that it should 
>> indicate the dissonant interval: (8)/7, 6/5, 4/3, 2/(0), the 8 and 0 
>> being omitted as redundant with the written bass, of course; this is 
>> what Dimitar describes, with a slightly different explanation. The 
>> main difference with the French system is that it does not 
>> specifically indicate _dominant_ sevenths, which may be viewed (by 
>> the French) as a shortcoming, or (by the others) as an advantage.
>> Nicolas Meeùs
>> Université Paris-Sorbonne
>> Le 9/02/2012 04:50, Ninov, Dimitar N a écrit :
>>> Dear Colleagues,
>>> My students were asking me why I wrote V2 instead of V4/2. I guess I had to ask them why they wrote V4/2 instead of V2. This is not a big deal, of course, but I wanted to bring to your attention the fact that number 4 is irrelevant to the logic of derivation of the abbreviated labels of seventh chords.
>>> The abbreviated labels are derived by two intervals: 1) the interval between the bass and the root on the one hand, and 2) the interval between the bass and the seventh on the other. Thus in root position the only number is 7, because the interval between the bass and the root is unison; in first inversion we have 6-5; in second inversion 4-3, and in third inversion the only number is 2, because the interval between the bass and the seventh is unison.
>>> Why 4? It shows the interval between the bass and the third of the seventh chord, which does not have to be shown unless we work in minor and use only figured bass with no Roman numerals.
>>> When I flip through the pages of some European and older American books of harmony (as well as some relatively new) the above explanation is provided. Author such as Piston, Tischler, Schoenberg, Horvitt, Cook, and all Russian theorists use 2 instead of 4/2, but the massive tendency in the US is to write 4-2. Is this tradition based on ignoring the logic of derivation, or is there something special that stands behind this label?
>>> I would appreciate any ideas in this regard.
>>> Best wishes,
>>> Dimitar
>>> Dr. Dimitar Ninov, Lecturer
>>> School of Music
>>> Texas State University
>>> 601 University Drive
>>> San Marcos, Texas 78666
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